本题目来源于试卷: Differential Calculus，类别为 IB数学
[问答题]
A curve C is givenho fopbx6u:p: vc,m.: btpxgj1 hx3wy 3k6u-0 xy the implicit equation $x-y+\sin (x y)=0$.
1. Show that $ \frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{1+y \cos (x y)}{1-x \cos (x y)}$.
2. The curve $x y=\pi$ intersects C at P and Q .
a. Find the coordinates of P and Q .
b. Given that the gradients of the tangents to C at P and Q are $m_{1}$ and $m_{2}$ respectively, show that $ m_{1} \cdot m_{2}=1$ .
3. Find the coordinates of the three points on C , nearest to the origin, where the tangent is parallel to the line y=x .
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